How do you find the complex conjugate of #[4 - sqrt(-3)]/ 2#?

1 Answer
Feb 5, 2016

Answer:

The complex conjugate of #(4-sqrt(-3))/2#
is
#2+sqrt(3)/2i#

Explanation:

First note
#color(white)("XXX")(4-sqrt(-3))/2 = 2-sqrt(3)/2i#

The complex conjugate of a complex number is
a number with
#color(white)("XXX")color(red)("the real component equal to the real component of the original number")#
and
#color(white)("XXX")color(blue)("the complex component equal in magnitude but opposite in sign.")#

So the complex conjugate of #color(red)(2)color(blue)(-sqrt(3)/2)i#
is #color(red)(2)color(blue)(+sqrt(3)/2)i#